Self-supporting interior structures modeling for buoyancy optimization of computational fabrication

Interior structures including lattice, porous, or cellular structures have been widely used in geometric design for 3D printing. It can not only reduce the weight of objects but also adjust the physical properties, such as stress, balance, and center of mass. In this work, we present a novel method for buoyant equilibrium and optimization of the material distribution inside an object, such that the 3D printed object satisfies prescribed constraints of mass properties. In particular, we introduce a mathematical method to describe the internal structure compactly, and prove that this compact formulation generates density-variable lattice structures to control the mass properties precisely. Additionally, this internal structure has shown itself to be capable of self-supporting in 3D printing processing. We demonstrate the effectiveness of our mathematically based method for generating interior patterns in the applications of optimizing shapes that stably float in liquids, and in improving mechanical stiffness.